The unique qualities of Spanish cheeses, such as the San Simón da Costa (SSC) cheese, are protected by the Protected Designation of Origin (PDO) status. The technological importance of chilled storage at 4 °C of vacuum-packaged (V) and natural (N) (unpackaged) cheeses was examined. For this purpose, the physico-chemical, biochemical, mechanical (puncture tests), viscoelastic (oscillatory and transient tests) and sensory properties of V and N cheeses were compared and analysed. During chilled storage, the caseins in V cheeses did not undergo proteolytic reactions. Low temperature maintained a low intensity of proteolytic phenomena for up to 6 months. Lipolysis was more intense in the N than in the V samples. The moisture content decreased in the N cheeses during chilled storage, and thus, the casein matrix concentration and ionic strength increased, resulting in an increase in the gel strength (S) parameter and complex modulus (G*), and the conformational stability−high stress amplitude (σmax). The low and similar values of the n’ and n’’ exponents (mechanical spectra) and the n parameter (transient tests) indicated the high degree of the temporal stability of the cheese network in both the N and V samples, irrespective of storage time. Likewise, the similar values of the phase angle (δ) for the N and V cheeses during storage indicate energy-stable bonds in the SSC cheese matrix. The attributes of the oral tactile phase (firmness, friability, gumminess, and microstructure perception), mechanical parameters and viscoelastic moduli enabled the discrimination of the packaged and unpackaged cheeses. Cheeses chilled and stored without packaging were awarded the highest scores for sensory attributes (preference) by trained panellists.